Blender’s animations are by default rendered as a sequence of perfectly still images.
While great for stop-motion and time-lapses, this is unrealistic, since fast-moving
objects do appear to be blurred in the direction of motion,
both in a movie frame and in a photograph from a real-world camera.

Vector Blur
is faster but sometimes has unwanted side-effects which are sometimes difficult to avoid.

Vector blur is a process done in compositing (post-render time), by rendering
the scene without any blur, plus a pass that has movement information for each pixel.
This information is a vector map which describes a 2D or 3D direction and magnitude.
The compositor uses that data to blur each pixel in the given direction.

To better grasp the concept, let us assume that we have a cube 2 units wide,
uniformly moving 1 unit to the right at each frame.
The scale beneath the cube helps in appreciating the movement of 1 Blender unit.

Frame 1 of the moving cube without Motion Blur.

Frame 2 of the moving cube without Motion Blur.

Frame 1 when Sampled Motion Blur is enabled and eight ‘intermediate’ frames are computed.
Shutter is set to 0.5 , thus the image eight samples are rendered between frame 1 and halfway to frame 2.

The effect of an increased shutter value.

Even further increased shutter value.

Values greater than 1 are physically impossible in a real-world camera, but can be used to exaggerate the effect.
Better results than those shown can be obtained by using higher samples than 8,
but, of course, since as many separate renders as samples are needed,
a Motion Blur render takes that many times more time than a non-Motion Blur one.